Neither the assertion that "God exists" nor that "the Bible is correct" have been independently proved without relying on the assumption of the other.

Counter-Counter-Arguments

Presuppositional apologists (primarily from the reformed school of theology) argue that circular reasoning is acceptable and necessary within a world-view and that circular reasoning is only un-acceptable when it presents a self-contradiction.
This is demonstrated by showing that the scientific worldview has certain assumptions about the universe and that those assumptions are based on observation but then observation is explained in terms of laws, which are themselves assumptions about the universe. This is, of course, acceptable because it is consistent in and of itself.

However, for this argument to be valid, the observer must consider the assumptions inviolable. Thousands of years ago, scientists assumed the sky, sun, stars, and moon all revolved around the earth, and developed "laws" (more properly called "theories") to explain this. Utilizing a circular thought process, scientists would be forced to incorporate their ideas within these geocentric theories. Utilizing a traditional scientific process, the scientist is permitted to completely reject these assumptions, and develop and test new hypotheses to explain the observations.

Right, and the argument is valid because the scientist does have assumptions that are inviolable. The law of non-contradiction for example. Or the veracity of the scientific method itself.